Completion time (from start to finish)of a building remodelling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.To be 99% sure that we will not be late in completing the project, we should request a completion time of ___ work-days.
A)211
B)207
C)223
D)200
E)250

Question

Quizplus · Accepted Answer

We need to find the completion time that ensures we will not be late 99% of the time. To find this, we need to look for the z-score that corresponds to the 99th percentile of the standard normal distribution. This z-score is approximately 2.33 (found using a standard normal table or calculator). We then use the formula:

z = (x - mu) / sigma

where x is the completion time we want to find, mu is the mean of 200 work-days, sigma is the standard deviation of 10 work-days, and z is the z-score of 2.33.

Solving for x, we get:

2.33 = (x - 200) / 10

23.3 = x - 200

x = 223.3

Therefore, we should request a completion time of 223 work-days (rounded to the nearest whole number) to be 99% sure that we will not be late. Choice C is the only option that matches this value.

Completion Time (From Start to Finish)of a Building Remodelling Project